With kitchen units and appliances in place do I remove plinths and fit tiles underneath then replace plinths over tiles (probably reducing the height of the plinth as well) or do I fit tiles up to plinths and appliances. Or is there another way to do it?

Do as you say for the plinths. With the appliances I would always remove, tile and replace.
If I absolutely had to tile upto the appliances (eg if the raised floor level meant the appliances would not fit back in - rare) then I always make sure the customer has a spare box of tiles as if you ever have to remove the appliance you will need to remove the tiles infront of the appliance which will need replacing.

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